US11831484B2 - Peak-to-average power ratio control - Google Patents
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- US11831484B2 US11831484B2 US17/794,715 US202017794715A US11831484B2 US 11831484 B2 US11831484 B2 US 11831484B2 US 202017794715 A US202017794715 A US 202017794715A US 11831484 B2 US11831484 B2 US 11831484B2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2614—Peak power aspects
- H04L27/2615—Reduction thereof using coding
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
- H04B7/046—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account
- H04B7/0465—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account taking power constraints at power amplifier or emission constraints, e.g. constant modulus, into account
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Definitions
- the present disclosure relates generally to the field of wireless communication. More particularly, it relates to controlling the peak-to-average power ratio (PAPR) of a wireless communication transmitter.
- PAPR peak-to-average power ratio
- a reduced peak-to-average power ratio may be seen as desirable.
- PAPR reduction may entail improved (e.g., increased) energy efficiency in radio parts of a wireless transmitter.
- PAPR reduction may, for example, be achieved by any suitable crest-factor reduction (CFR) technique (e.g., clipping and/or filtering).
- CFR crest-factor reduction
- Example disadvantageous effects include increased computational complexity, increased latency, and increased error vector magnitude (EVM) of the communication channel.
- EVM error vector magnitude
- the physical product may comprise one or more parts, such as controlling circuitry in the form of one or more controllers, one or more processors, or the like.
- PAPR PAPR
- a PAPR reduction may correspond to a crest factor reduction
- PAPR control may correspond to crest factor control, etc.
- a first aspect is a method of a wireless communication transmitter for peak-to-average power ratio (PAPR) control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements.
- PAPR peak-to-average power ratio
- the method comprises applying a PAPR cost function ⁇ (x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission (e.g., frequency-domain samples), wherein a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter ⁇ for tuning.
- the method also comprises selecting a value for the parameter ⁇ , wherein the selection comprises performing a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter, and selecting a precoding for the collection of samples as a solution to an optimization problem for the selected value for the parameter ⁇ .
- the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and solving the optimization problem comprises using the proximal operator of the PAPR cost function.
- the PAPR cost function has an infinite value in the interval [a, ⁇ ).
- the PAPR cost function is a log-barrier function or a Huber function.
- the proximal operator of the PAPR cost function is defined as
- the optimization problem is
- g ⁇ ( x ) ⁇ 0 for ⁇ error ⁇ free ⁇ channel ⁇ transfer ⁇ otherwise .
- solving the optimization problem comprises applying an iterative optimization algorithm, wherein each iteration uses the proximal operator.
- the iterative optimization algorithm is a Douglas-Rachford operator splitting algorithm and/or an alternating direction method of multipliers—ADMM.
- the at least one other characteristic of the wireless communication transmitter comprises an error vector magnitude (EVM).
- EVM error vector magnitude
- performing the trade-off comprises increasing PAPR to improve the at least one other characteristic.
- selecting the value for the parameter ⁇ comprises addressing a look-up table of values for the parameter based on the number of antenna elements M, the number of time-domain signal samples N, and use case requirements for PAPR and the at least one other characteristic of the wireless communication transmitter.
- the method further comprises solving the optimization problem for a plurality of values of the parameter 2 , and populating the look-up table accordingly.
- the method further comprises transmitting the N time-domain signal samples via the M antenna elements using the selected precoding.
- a second aspect is a computer program product comprising a non-transitory computer readable medium, having thereon a computer program comprising program instructions.
- the computer program is loadable into a data processing unit and configured to cause execution of the method according to the first aspect when the computer program is run by the data processing unit.
- a third aspect is an apparatus for a wireless communication transmitter and for peak-to-average power ratio (PAPR) control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements.
- PAPR peak-to-average power ratio
- the apparatus comprises controlling circuitry configured to cause application of a PAPR cost function ⁇ (x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission, wherein a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter ⁇ for tuning.
- a PAPR cost function ⁇ (x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission, wherein a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter ⁇ for tuning.
- the controlling circuitry is also configured to cause selection of a value for the parameter ⁇ , wherein the selection comprises performance of a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter, and selection of a precoding for the collection of samples as a solution to an optimization problem for the selected value for the parameter ⁇ .
- the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and solving the optimization problem comprises using the proximal operator of the PAPR cost function.
- a fourth aspect is a wireless communication transmitter comprising the apparatus of the third aspect.
- a fifth aspect is a radio base station comprising the wireless communication transmitter of the fourth aspect.
- any of the above aspects may additionally have features identical with or corresponding to any of the various features as explained above for any of the other aspects.
- the collection of samples for transmission may be time-domain signal samples for transmission and/or frequency-domain samples for transmission.
- the collection of samples for transmission may be a collection of frequency-domain samples for transmission corresponding to the N time-domain signal samples for transmission in an orthogonal frequency division multiplex (OFDM) scenario.
- OFDM orthogonal frequency division multiplex
- the collection of samples for transmission may, for example, be NM samples; e.g., arranged in a vector.
- An advantage of some embodiments is that alternative approaches for PAPR control are provided.
- An advantage of some embodiments is that energy efficiency may be improved by PAPR reduction.
- An advantage of some embodiments is that computational complexity is unchanged (or very slightly increased) compared to some prior art approaches for PAPR reduction.
- PAPR control may be improved.
- PAPR control according to some embodiments may enable PAPR reduction subject to trade-off against one or more disadvantageous effects (e.g., increased EVM).
- such trade-off may be conditioned on predefined requirements (constraints) regarding the one or more disadvantageous effects.
- the predefined requirements may, for example, be associated with a wireless communication use case under consideration.
- FIG. 1 is a flowchart illustrating example method steps according to some embodiments
- FIG. 2 is a plot illustrating example penalty functions according to some embodiments
- FIG. 3 is a pair of simulation plots illustrating example EVM and PAPR distributions achievable by application of some embodiments
- FIG. 4 is a schematic block diagram illustrating an example communication scenario according to some embodiments.
- FIG. 5 is a schematic block diagram illustrating an example apparatus according to some embodiments.
- FIG. 6 is a schematic drawing illustrating an example computer readable medium according to some embodiments.
- FIG. 1 illustrates an example method 100 according to some embodiments.
- the method may be performed by an apparatus such as a wireless communication device, a wireless communication transmitter, a network node, or a radio base station.
- an apparatus such as a wireless communication device, a wireless communication transmitter, a network node, or a radio base station.
- the method is for PAPR control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements.
- N Typically N>1 and M>1.
- a large antenna system scenario e.g., a massive-MIMO scenario
- the method is applied in a scenario wherein the number N of time-domain signal samples for transmission is relatively large; e.g., N>10, N>100, or N>1000.
- the number N may typically equal a number of points used in an inverse fast Fourier transform (IFFT) to generate an OFDM symbol.
- IFFT inverse fast Fourier transform
- the N time-domain signal samples may, for example, be intended for one or more wireless communication receivers, each having one or more receiver antennas.
- the number M of antenna elements is larger than the number of users (wherein users may refer to the number of receivers, for example). This provides a null space in relation to the channel, which can be utilized for optimization and/or trade-off as exemplified in the following.
- the N time-domain signal samples may be N time-domain signal samples of an orthogonal frequency division multiplex (OFDM) symbol; i.e., an OFDM-symbol of length N, and each of the M antenna elements may transmit a corresponding OFDM-symbol using N sub-carriers.
- OFDM orthogonal frequency division multiplex
- a PAPR cost function ⁇ (x) is applied to a collection of samples for transmission.
- the vector x may be seen as representing a precoded baseband vector for transmission, and it may be seen as an aim for the method 100 to find a suitable precoding (i.e., a suitable x; provided the signal information content is predetermined).
- a suitable precoding may, for example, be a precoding that keeps the PAPR as low as possible (or lower than a PAPR requirement) while also meeting a requirement of at least one other characteristic of the wireless communication transmitter (e.g., one or more of EVM, complexity, and latency).
- other characteristic of the wireless communication transmitter may include one or more of EVM, complexity, and latency.
- x does not necessarily have to be represented as a vector.
- Other possibilities include various matrix representations, for example.
- the PAPR cost function ⁇ (x) has a closed form proximal operator and is differentiable in the interval [0, a[. Furthermore, the proximal operator of the PAPR cost function has a parameter ⁇ for tuning. In some embodiments, the PAPR cost function has an infinite value in the interval [a, ⁇ ).
- the value a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample. This may alternatively be expressed in terms of a parameter value P which corresponds to a maximum allowable power.
- PAPR cost functions examples include a log-barrier function and a Huber function.
- the transfer function A can be any suitable transfer function or the identity matrix.
- the proximal operator of the PAPR cost function ⁇ (x) is expressed as
- pro ⁇ x ⁇ ⁇ f ( v ) arg ⁇ min x ⁇ ( f ⁇ ( x ) + 1 2 ⁇ ⁇ ⁇ ⁇ x - v ⁇ 2 2 ) .
- ) can be obtained as follows:
- the proximal operator of the log-barrier function can be expressed in closed form where the parameter ⁇ survives and is available for tuning.
- An advantage of having the parameter ⁇ available for tuning is that a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter (e.g., one or more of EVM, complexity, and latency) is possible.
- the parameter ⁇ may be seen as a trade-off parameter.
- a value for the parameter ⁇ is selected.
- the selection comprises performing a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter as illustrated by sub-step 142 .
- the trade-off may, for example, comprise—in comparison to a specific PAPR value and corresponding values of at least one other characteristic of the wireless communication transmitter—settling for an increased PAPR in exchange for an improvement of the corresponding value of at least one of the other characteristics of the wireless communication transmitter (e.g., decreased computational complexity, decreased latency, and/or decreased EVM of the communication channel).
- the specific PAPR value may be a PAPR value that would result from application of any prior art method, for example, or from any method wherein tuning is not possible.
- the trade-off may comprise adaptation to one or more use case requirements for PAPR and the at least one other characteristic of the wireless communication transmitter.
- a wireless communication use case may require one or more of: that PAPR is below a PAPR threshold, that EVM is below an EVM threshold, that computational complexity is below a complexity threshold, and that latency is below a latency threshold.
- Such use case requirements may, for example be set by wireless communication standardization (e.g., PAPR, EVM, latency) and/or by product specifications (e.g., PAPR, complexity).
- a precoding is selected for the samples to be transmitted. Selecting precoding may comprise selecting amplitudes and/or phases for the frequency-domain samples.
- the precoding is selected as a solution to an optimization problem for the selected value for the parameter ⁇ .
- the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function.
- the optimization problem may comprise minimization the PAPR cost function alone.
- the optimization problem may comprise minimization of an overall cost function comprising the PAPR cost function as a first term and another cost function g(x) as a second term:
- g(x) may be a channel transfer penalty function.
- the channel transfer penalty function may be defined as
- g ⁇ ( x ) ⁇ 0 for ⁇ error ⁇ free ⁇ channel ⁇ transfer ⁇ otherwise .
- solving the optimization problem may comprise using the proximal operator of the PAPR cost function.
- solving the optimization problem may comprise applying an iterative optimization algorithm, wherein each iteration uses the proximal operator.
- Example iterative optimization algorithms include the Douglas-Rachford operator splitting algorithm and the alternating direction method of multipliers (ADMM).
- the parameter ⁇ represents a step size of the proximal operator variable and/or a step size used in the Douglas-Rachford splitting algorithm and/or a step size of the alternating direction method of multipliers (ADMM).
- the method may further comprise transmitting the N time-domain signal samples via the M antenna elements using the selected precoding, as illustrated by optional step 160 .
- step 140 comprises solving the optimization problem in the process of selecting a value for the parameter ⁇ , as illustrated by optional sub-step 143 .
- the optimization problem is solved beforehand in a pre-computation step for a plurality of values of the parameter ⁇ , as illustrated by optional step 120 , to provide corresponding pre-determined precoding alternatives and/or corresponding pre-determined values of the at least one other characteristic of the wireless communication transmitter.
- step 140 may comprise selecting the value for the parameter ⁇ based on corresponding pre-determined values of the at least one other characteristic of the wireless communication transmitter, and step 150 may comprise selecting the precoding based on the pre-determined precoding alternatives.
- the value for the parameter ⁇ may be selected as one of the plurality of values used in the pre-computation step; such that the corresponding pre-determined values of the at least one other characteristic of the wireless communication transmitter meet the applicable requirements (e.g., of a use case as elaborated on above). Then, the precoding may be selected as the corresponding pre-determined precoding alternative.
- the value for the parameter may be selected as an interpolation between two of the plurality of values used in the pre-computation step; such that the values of the at least one other characteristic of the wireless communication transmitter will probably meet the applicable requirements.
- the precoding may be selected as an interpolation between the corresponding two pre-determined precoding alternatives.
- the method comprises populating a look-up table (as illustrated by optional step 130 ) based on a plurality of solutions to the optimization problem using a corresponding plurality of values of the parameter ⁇ . In some embodiments, this is performed for various applicable values of the number of antenna elements M and/or the number of time-domain signal samples N. It should be noted that numerous other implementation alternatives than a look-up table are possible.
- the plurality of solutions to the optimization problem may comprise those achieved in the pre-computation step 120 .
- the plurality of solutions to the optimization problem may comprise solutions achieved in sub-step 143 . The latter may lead to successively populating the look-up table during repeated execution of the method 100 .
- the look-up table When the look-up table is sufficiently populated, it may be used to perform the trade-off of sub-step 142 for selection of the value for the parameter 2 , as illustrated by optional sub-step 144 .
- the value for the parameter ⁇ may be selected as one of the plurality of values used to populate the look-up table; by addressing the look-up table based on the number of antenna elements M, the number of time-domain signal samples N, and use case requirements for PAPR and the at least one other characteristic of the wireless communication transmitter.
- PAPR cost function is defined by the indicator function
- the indicator function has a proximal operator which is non-differentiable. Furthermore, the tuning parameter vanishes during solution to the optimization problem according to the approach described therein.
- the x-axis illustrates the signal amplitude for one time-domain signal sample [Ax] i with the maximum allowable value a shown at 203
- the y-axis illustrates the value of the function ⁇ (x), which denotes the cost value of the sample, i.e., ⁇ log(a ⁇ [Ax] i ) for the log-barrier function.
- FIG. 3 illustrates example EVM and PAPR distributions achievable by application of some embodiments.
- g ⁇ ( x ) ⁇ 0 for ⁇ error ⁇ free ⁇ channel ⁇ transfer ⁇ otherwise .
- the x-axis represents the EVM value (in % of the reference sample magnitude) and extends from 0% to 40%.
- the y-axis represents the probability density function value and extends from 0 to 1.4.
- the x-axis represents the PAPR value (in dB) and extends from 0.5 to 3.0.
- the y-axis represents the probability density function value and extends from 0 to 10.
- FIG. 4 schematically illustrates an example communication scenario where some embodiments may be applicable.
- the left-hand side of FIG. 4 relates to a wireless communication transmitter having M antenna elements, and the right-hand side of FIG. 4 relates to a plurality of K wireless communication receivers.
- the wireless communication transmitter and the plurality of wireless communication receivers are separated by a frequency-selective channel (CH) 450 .
- CH frequency-selective channel
- a number of N vector messages s i ⁇ K ⁇ 1 , i 1, . . . , N—corresponding to N flat fading sub-channels and each with a length K, corresponding to K receivers (users)—represent the information to be transmitted and are input to the wireless communication transmitter as illustrated at 408 , 409 .
- DP digital precoder
- Each transmitter path 441 , 442 , 443 may, for example, comprise a parallel-to-serial converter, a cyclic prefix pre-pender, and a power amplifier.
- Each of the wireless communication receivers may comprise an antenna 488 , 489 and a receiver path (RP) 491 , 492 .
- Each receiver path may, for example, comprise a cyclic prefix remover, a serial-to-parallel converter, and a fast Fourier transform (FFT) for recovering the N frequency-domain samples.
- FFT fast Fourier transform
- the wireless communication transmitter also comprises a controller (CNTR) 400 receiving the N frequency-domain sample vectors x i 418 , 419 .
- the controller may, for example, be configured to execute (or cause execution of) one or more of the method steps as described above in connection with FIG. 1 .
- the controller may be configured to select precoding as described in connection with FIG. 1 and control the digital precoder 410 accordingly, as illustrated by control signal 401 in FIG. 4 .
- the controller may be configured to control other parts of the transmitter (e.g., components of the transmitter paths 441 , 442 , 443 ) to enforce the selected precoding.
- FIG. 5 schematically illustrates an example apparatus 510 according to some embodiments.
- the apparatus may be comprised, or comprisable, in one or more of a wireless communication device, a wireless communication transmitter, a network node, and a radio base station. Furthermore, the apparatus may be configured to execute (or cause execution of) one or more of the method steps as described above in connection with FIG. 1 .
- the apparatus is for PAPR control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements (compare with FIG. 4 ).
- the N time-domain signal samples may, for example, be intended for one or more wireless communication receivers, each having one or more receiver antennas.
- the N time-domain signal samples may be N time-domain signal samples of an orthogonal frequency division multiplex (OFDM) symbol; i.e., an OFDM-symbol of length N, and each of the M antenna elements may transmit a corresponding OFDM-symbol using N sub-carriers.
- OFDM orthogonal frequency division multiplex
- the apparatus comprises a controller 500 (CNTR; e.g., controlling circuitry or a control module—compare with 400 of FIG. 4 ).
- CNTR controlling circuitry or a control module
- the controller may comprise or be otherwise associated with (e.g., connected, or connectable, to) cost function circuitry or a cost function module (CF) 501 .
- the cost function circuitry or a cost function module may, for example, be a memory configured to store one or more cost functions and provide a suitable cost function for application.
- the controller is also configured to cause selection (compare with step 140 of FIG. 1 ) of a value for the parameter ⁇ , wherein the selection comprises performance of a trade-off (compare with step 142 of FIG. 1 ) between PAPR and at least one other characteristic of the wireless communication transmitter.
- the controller may comprise or be otherwise associated with (e.g., connected, or connectable, to) a tuning selector (TS; e.g., tuning selection circuitry or a tuning selection module) 502 .
- the tuning selector may be configured to select the value for the parameter ⁇ .
- the controller is also configured to cause selection (compare with step 150 of FIG. 1 ) of a precoding for the samples as a solution to an optimization problem for the selected value for the parameter ⁇ , wherein the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and wherein solving the optimization problem comprises using the proximal operator of the PAPR cost function.
- the controller may comprise or be otherwise associated with (e.g., connected, or connectable, to) a precoding selector (PS; e.g., precoding selection circuitry or a precoding selection module) 503 .
- the precoding selector may be configured to select the precoding for the samples.
- the controller may also be configured to cause transmission (compare with optional step 160 of FIG. 1 ) of the N time-domain signal samples via the M antenna elements using the selected precoding.
- the controller may be associated with (e.g., connected, or connectable, to) a transmitter (TX; e.g., transmission circuitry or a transmission module) 530 .
- TX e.g., transmission circuitry or a transmission module
- the transmitter which may—or may not—be comprised in the apparatus 510 , may be configured to transmit the N time-domain signal samples via the M antenna elements using the selected precoding.
- the controller may also be configured to cause solving (compare with optional steps 120 and 143 of FIG. 1 ) of the optimization problem for one or more values of the parameter ⁇ .
- the controller may comprise or be otherwise associated with (e.g., connected, or connectable, to) an optimizer (OPT; e.g., optimization circuitry or an optimization module) 505 .
- the optimizer may be configured to solve the optimization problem for one or more values of the parameter ⁇ .
- the controller may also be configured to cause population and/or addressing (compare with optional steps 130 and 144 of FIG. 1 ) of a look-up table (LUT; e.g., look-up table circuitry or a look-up table module) 504 comprised in—or be otherwise associated with (e.g., connected, or connectable, to) the controller 500 .
- LUT look-up table
- the optimization problem may be defined as
- ⁇ (x) may relate to a requirement that the transmitted amplitude cannot exceed a threshold a and g(x) may relate to a requirement of correct channel transfer of the transmitted information content.
- the cost functions ⁇ (x) and g(x) may both be convex functions.
- ⁇ (x) may be an indicator function over the ⁇ -norm (or max-norm) bounded set
- g(x) may be an indicator function over the affine set (e.g., a set of all solutions to a system of linear equations). This may be explicitly formulated as:
- Z (k-1) represents v
- X (k) represents x
- the parameter has the role of determining a step size for each iteration (distance from v towards optimum—e.g., minimum—of ⁇ (x)).
- an optimization problem suitable for the context of “Democratic representations” (referenced above) may be formulated as:
- the described embodiments and their equivalents may be realized in software or hardware or a combination thereof.
- the embodiments may be performed by general purpose circuitry. Examples of general purpose circuitry include digital signal processors (DSP), central processing units (CPU), co-processor units, field programmable gate arrays (FPGA) and other programmable hardware.
- DSP digital signal processors
- CPU central processing units
- FPGA field programmable gate arrays
- the embodiments may be performed by specialized circuitry, such as application specific integrated circuits (ASIC).
- ASIC application specific integrated circuits
- the general purpose circuitry and/or the specialized circuitry may, for example, be associated with or comprised in an apparatus such as a wireless communication device, a wireless communication transmitter, a network node, or a radio base station.
- Embodiments may appear within an electronic apparatus (such as a wireless communication device, a wireless communication transmitter, a network node, or a radio base station) comprising arrangements, circuitry, and/or logic according to any of the embodiments described herein.
- an electronic apparatus such as a wireless communication device, a wireless communication transmitter, a network node, or a radio base station
- an electronic apparatus may be configured to perform methods according to any of the embodiments described herein.
- a computer program product comprises a tangible, or non-tangible, computer readable medium such as, for example a universal serial bus (USB) memory, a plug-in card, an embedded drive or a read only memory (ROM).
- FIG. 6 illustrates an example computer readable medium in the form of a compact disc (CD) ROM 600 .
- the computer readable medium has stored thereon a computer program comprising program instructions.
- the computer program is loadable into a data processor (PROC; e.g., data processing circuitry or a data processing unit) 620 , which may, for example, be comprised in a wireless communication device, a wireless communication transmitter, a network node, or a radio base station 610 .
- PROC data processor
- the computer program When loaded into the data processor, the computer program may be stored in a memory (MEM) 630 associated with or comprised in the data processor. According to some embodiments, the computer program may, when loaded into and run by the data processor, cause execution of method steps according to, for example, any of the methods as illustrated in FIG. 1 or otherwise described herein.
- MEM memory
- the computer program may, when loaded into and run by the data processor, cause execution of method steps according to, for example, any of the methods as illustrated in FIG. 1 or otherwise described herein.
- the method embodiments described herein discloses example methods through steps being performed in a certain order. However, it is recognized that these sequences of events may take place in another order without departing from the scope of the claims. Furthermore, some method steps may be performed in parallel even though they have been described as being performed in sequence. Thus, the steps of any methods disclosed herein do not have to be performed in the exact order disclosed, unless a step is explicitly described as following or preceding another step and/or where it is implicit that a step must follow or precede another step.
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Abstract
Description
wherein g(x) is a channel transfer penalty function.
is a given complex vector, and
denotes the vector of variables for precoding, the proximal operator of the log-barrier function expressed as ƒ(x)=Σi=1 L−log(a−|xi|) can be obtained as follows:
since the first term is independent of the phase vector φ and the second term is minimized for φi=θi, i=1, . . . , L. It is noteworthy that the last objective function is convex, differentiable, and also separable in respect of ri for i=1, . . . , L. The minimum can be found by invoking the first derivative test:
-
- Possibility to differentiate cost functions and their proximal operators which may simplify optimization and/or make more optimization algorithms possible to apply.
- Presence of a tuning parameter in the solution to the optimization problem which enables trade-off between PAPR and at least one other characteristic of the wireless communication transmitter.
with the log-barrier function as ƒ(x) and
where ƒ(x) may relate to a requirement that the transmitted amplitude cannot exceed a threshold a and g(x) may relate to a requirement of correct channel transfer of the transmitted information content. Typically, the cost functions ƒ(x) and g(x) may both be convex functions.
Algorithm 1 Douglas-Rachford Splitting |
Input: Z(0) = 0 |
1: | function DOUGLAS-RACHFORD(X(0)) | ||
2: | for k = 1, 2, . . . do | ||
3: | X(k) ← proxλf(Z(k−1)) | ||
4: | Z(k) ← Z(k−1) + proxλg(2X(k) − Z(k−1)) − X(k) | ||
5: | end for | ||
6: | return X(k) | ||
7: | end function | ||
and k=0, 1, 2, . . . represents the iteration count. In this algorithm, the parameter has the role of determining a step size for each iteration (distance from v towards optimum—e.g., minimum—of ƒ(x)).
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US20100322090A1 (en) * | 2009-06-18 | 2010-12-23 | Qualcomm Incorporated | Power scaling for multi-carrier high-speed uplink packet access |
WO2018147775A1 (en) | 2017-02-08 | 2018-08-16 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and arrangement for signal distortion mitigation |
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